Identifier
Mp00119: Dyck paths —to 321-avoiding permutation (Krattenthaler)⟶ Permutations
Mp00086: Permutations —first fundamental transformation⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Images
=>
Cc0005;cc-rep-0Cc0010;cc-rep-3
[1,0]=>[1]=>[1]=>[.,.] [1,0,1,0]=>[1,2]=>[1,2]=>[.,[.,.]] [1,1,0,0]=>[2,1]=>[2,1]=>[[.,.],.] [1,0,1,0,1,0]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]] [1,0,1,1,0,0]=>[1,3,2]=>[1,3,2]=>[.,[[.,.],.]] [1,1,0,0,1,0]=>[2,1,3]=>[2,1,3]=>[[.,.],[.,.]] [1,1,0,1,0,0]=>[2,3,1]=>[3,2,1]=>[[[.,.],.],.] [1,1,1,0,0,0]=>[3,1,2]=>[2,3,1]=>[[.,[.,.]],.] [1,0,1,0,1,0,1,0]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]] [1,0,1,0,1,1,0,0]=>[1,2,4,3]=>[1,2,4,3]=>[.,[.,[[.,.],.]]] [1,0,1,1,0,0,1,0]=>[1,3,2,4]=>[1,3,2,4]=>[.,[[.,.],[.,.]]] [1,0,1,1,0,1,0,0]=>[1,3,4,2]=>[1,4,3,2]=>[.,[[[.,.],.],.]] [1,0,1,1,1,0,0,0]=>[1,4,2,3]=>[1,3,4,2]=>[.,[[.,[.,.]],.]] [1,1,0,0,1,0,1,0]=>[2,1,3,4]=>[2,1,3,4]=>[[.,.],[.,[.,.]]] [1,1,0,0,1,1,0,0]=>[2,1,4,3]=>[2,1,4,3]=>[[.,.],[[.,.],.]] [1,1,0,1,0,0,1,0]=>[2,3,1,4]=>[3,2,1,4]=>[[[.,.],.],[.,.]] [1,1,0,1,0,1,0,0]=>[2,3,4,1]=>[4,2,3,1]=>[[[.,.],[.,.]],.] [1,1,0,1,1,0,0,0]=>[2,4,1,3]=>[3,2,4,1]=>[[[.,.],[.,.]],.] [1,1,1,0,0,0,1,0]=>[3,1,2,4]=>[2,3,1,4]=>[[.,[.,.]],[.,.]] [1,1,1,0,0,1,0,0]=>[3,1,4,2]=>[3,4,1,2]=>[[.,[.,.]],[.,.]] [1,1,1,0,1,0,0,0]=>[3,4,1,2]=>[2,4,3,1]=>[[.,[[.,.],.]],.] [1,1,1,1,0,0,0,0]=>[4,1,2,3]=>[2,3,4,1]=>[[.,[.,[.,.]]],.] [1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]] [1,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,4]=>[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]] [1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>[1,2,4,3,5]=>[.,[.,[[.,.],[.,.]]]] [1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,3]=>[1,2,5,4,3]=>[.,[.,[[[.,.],.],.]]] [1,0,1,0,1,1,1,0,0,0]=>[1,2,5,3,4]=>[1,2,4,5,3]=>[.,[.,[[.,[.,.]],.]]] [1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,5]=>[1,3,2,4,5]=>[.,[[.,.],[.,[.,.]]]] [1,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4]=>[1,3,2,5,4]=>[.,[[.,.],[[.,.],.]]] [1,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,5]=>[1,4,3,2,5]=>[.,[[[.,.],.],[.,.]]] [1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,2]=>[1,5,3,4,2]=>[.,[[[.,.],[.,.]],.]] [1,0,1,1,0,1,1,0,0,0]=>[1,3,5,2,4]=>[1,4,3,5,2]=>[.,[[[.,.],[.,.]],.]] [1,0,1,1,1,0,0,0,1,0]=>[1,4,2,3,5]=>[1,3,4,2,5]=>[.,[[.,[.,.]],[.,.]]] [1,0,1,1,1,0,0,1,0,0]=>[1,4,2,5,3]=>[1,4,5,2,3]=>[.,[[.,[.,.]],[.,.]]] [1,0,1,1,1,0,1,0,0,0]=>[1,4,5,2,3]=>[1,3,5,4,2]=>[.,[[.,[[.,.],.]],.]] [1,0,1,1,1,1,0,0,0,0]=>[1,5,2,3,4]=>[1,3,4,5,2]=>[.,[[.,[.,[.,.]]],.]] [1,1,0,0,1,0,1,0,1,0]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]] [1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4]=>[2,1,3,5,4]=>[[.,.],[.,[[.,.],.]]] [1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,5]=>[2,1,4,3,5]=>[[.,.],[[.,.],[.,.]]] [1,1,0,0,1,1,0,1,0,0]=>[2,1,4,5,3]=>[2,1,5,4,3]=>[[.,.],[[[.,.],.],.]] [1,1,0,0,1,1,1,0,0,0]=>[2,1,5,3,4]=>[2,1,4,5,3]=>[[.,.],[[.,[.,.]],.]] [1,1,0,1,0,0,1,0,1,0]=>[2,3,1,4,5]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]] [1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,4]=>[3,2,1,5,4]=>[[[.,.],.],[[.,.],.]] [1,1,0,1,0,1,0,0,1,0]=>[2,3,4,1,5]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]] [1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.] [1,1,0,1,0,1,1,0,0,0]=>[2,3,5,1,4]=>[4,2,3,5,1]=>[[[.,.],[.,[.,.]]],.] [1,1,0,1,1,0,0,0,1,0]=>[2,4,1,3,5]=>[3,2,4,1,5]=>[[[.,.],[.,.]],[.,.]] [1,1,0,1,1,0,0,1,0,0]=>[2,4,1,5,3]=>[4,2,5,1,3]=>[[[.,.],[.,.]],[.,.]] [1,1,0,1,1,0,1,0,0,0]=>[2,4,5,1,3]=>[3,2,5,4,1]=>[[[.,.],[[.,.],.]],.] [1,1,0,1,1,1,0,0,0,0]=>[2,5,1,3,4]=>[3,2,4,5,1]=>[[[.,.],[.,[.,.]]],.] [1,1,1,0,0,0,1,0,1,0]=>[3,1,2,4,5]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]] [1,1,1,0,0,0,1,1,0,0]=>[3,1,2,5,4]=>[2,3,1,5,4]=>[[.,[.,.]],[[.,.],.]] [1,1,1,0,0,1,0,0,1,0]=>[3,1,4,2,5]=>[3,4,1,2,5]=>[[.,[.,.]],[.,[.,.]]] [1,1,1,0,0,1,0,1,0,0]=>[3,1,4,5,2]=>[3,5,1,4,2]=>[[.,[.,.]],[[.,.],.]] [1,1,1,0,0,1,1,0,0,0]=>[3,1,5,2,4]=>[3,4,1,5,2]=>[[.,[.,.]],[[.,.],.]] [1,1,1,0,1,0,0,0,1,0]=>[3,4,1,2,5]=>[2,4,3,1,5]=>[[.,[[.,.],.]],[.,.]] [1,1,1,0,1,0,0,1,0,0]=>[3,4,1,5,2]=>[4,5,3,1,2]=>[[[.,[.,.]],.],[.,.]] [1,1,1,0,1,0,1,0,0,0]=>[3,4,5,1,2]=>[2,5,3,4,1]=>[[.,[[.,.],[.,.]]],.] [1,1,1,0,1,1,0,0,0,0]=>[3,5,1,2,4]=>[2,4,3,5,1]=>[[.,[[.,.],[.,.]]],.] [1,1,1,1,0,0,0,0,1,0]=>[4,1,2,3,5]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]] [1,1,1,1,0,0,0,1,0,0]=>[4,1,2,5,3]=>[2,4,5,1,3]=>[[.,[.,[.,.]]],[.,.]] [1,1,1,1,0,0,1,0,0,0]=>[4,1,5,2,3]=>[4,3,5,1,2]=>[[[.,.],[.,.]],[.,.]] [1,1,1,1,0,1,0,0,0,0]=>[4,5,1,2,3]=>[2,3,5,4,1]=>[[.,[.,[[.,.],.]]],.] [1,1,1,1,1,0,0,0,0,0]=>[5,1,2,3,4]=>[2,3,4,5,1]=>[[.,[.,[.,[.,.]]]],.] [1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]] [1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>[.,[.,[.,[.,[[.,.],.]]]]] [1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>[.,[.,[.,[[.,.],[.,.]]]]] [1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,4]=>[1,2,3,6,5,4]=>[.,[.,[.,[[[.,.],.],.]]]] [1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,4,5]=>[1,2,3,5,6,4]=>[.,[.,[.,[[.,[.,.]],.]]]] [1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>[.,[.,[[.,.],[.,[.,.]]]]] [1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>[.,[.,[[.,.],[[.,.],.]]]] [1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,3,6]=>[1,2,5,4,3,6]=>[.,[.,[[[.,.],.],[.,.]]]] [1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,6,3]=>[1,2,6,4,5,3]=>[.,[.,[[[.,.],[.,.]],.]]] [1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,3,5]=>[1,2,5,4,6,3]=>[.,[.,[[[.,.],[.,.]],.]]] [1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,3,4,6]=>[1,2,4,5,3,6]=>[.,[.,[[.,[.,.]],[.,.]]]] [1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,5,3,6,4]=>[1,2,5,6,3,4]=>[.,[.,[[.,[.,.]],[.,.]]]] [1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,5,6,3,4]=>[1,2,4,6,5,3]=>[.,[.,[[.,[[.,.],.]],.]]] [1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,3,4,5]=>[1,2,4,5,6,3]=>[.,[.,[[.,[.,[.,.]]],.]]] [1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>[.,[[.,.],[.,[.,[.,.]]]]] [1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>[.,[[.,.],[.,[[.,.],.]]]] [1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>[.,[[.,.],[[.,.],[.,.]]]] [1,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,6,4]=>[1,3,2,6,5,4]=>[.,[[.,.],[[[.,.],.],.]]] [1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,4,5]=>[1,3,2,5,6,4]=>[.,[[.,.],[[.,[.,.]],.]]] [1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,2,5,6]=>[1,4,3,2,5,6]=>[.,[[[.,.],.],[.,[.,.]]]] [1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,2,6,5]=>[1,4,3,2,6,5]=>[.,[[[.,.],.],[[.,.],.]]] [1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,2,6]=>[1,5,3,4,2,6]=>[.,[[[.,.],[.,.]],[.,.]]] [1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,2]=>[1,6,3,4,5,2]=>[.,[[[.,.],[.,[.,.]]],.]] [1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,2,5]=>[1,5,3,4,6,2]=>[.,[[[.,.],[.,[.,.]]],.]] [1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,2,4,6]=>[1,4,3,5,2,6]=>[.,[[[.,.],[.,.]],[.,.]]] [1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,2,6,4]=>[1,5,3,6,2,4]=>[.,[[[.,.],[.,.]],[.,.]]] [1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,5,6,2,4]=>[1,4,3,6,5,2]=>[.,[[[.,.],[[.,.],.]],.]] [1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,6,2,4,5]=>[1,4,3,5,6,2]=>[.,[[[.,.],[.,[.,.]]],.]] [1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,2,3,5,6]=>[1,3,4,2,5,6]=>[.,[[.,[.,.]],[.,[.,.]]]] [1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,2,3,6,5]=>[1,3,4,2,6,5]=>[.,[[.,[.,.]],[[.,.],.]]] [1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,2,5,3,6]=>[1,4,5,2,3,6]=>[.,[[.,[.,.]],[.,[.,.]]]] [1,0,1,1,1,0,0,1,0,1,0,0]=>[1,4,2,5,6,3]=>[1,4,6,2,5,3]=>[.,[[.,[.,.]],[[.,.],.]]] [1,0,1,1,1,0,0,1,1,0,0,0]=>[1,4,2,6,3,5]=>[1,4,5,2,6,3]=>[.,[[.,[.,.]],[[.,.],.]]] [1,0,1,1,1,0,1,0,0,0,1,0]=>[1,4,5,2,3,6]=>[1,3,5,4,2,6]=>[.,[[.,[[.,.],.]],[.,.]]] [1,0,1,1,1,0,1,0,0,1,0,0]=>[1,4,5,2,6,3]=>[1,5,6,4,2,3]=>[.,[[[.,[.,.]],.],[.,.]]] [1,0,1,1,1,0,1,0,1,0,0,0]=>[1,4,5,6,2,3]=>[1,3,6,4,5,2]=>[.,[[.,[[.,.],[.,.]]],.]] [1,0,1,1,1,0,1,1,0,0,0,0]=>[1,4,6,2,3,5]=>[1,3,5,4,6,2]=>[.,[[.,[[.,.],[.,.]]],.]] [1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,2,3,4,6]=>[1,3,4,5,2,6]=>[.,[[.,[.,[.,.]]],[.,.]]] [1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5,2,3,6,4]=>[1,3,5,6,2,4]=>[.,[[.,[.,[.,.]]],[.,.]]] [1,0,1,1,1,1,0,0,1,0,0,0]=>[1,5,2,6,3,4]=>[1,5,4,6,2,3]=>[.,[[[.,.],[.,.]],[.,.]]] [1,0,1,1,1,1,0,1,0,0,0,0]=>[1,5,6,2,3,4]=>[1,3,4,6,5,2]=>[.,[[.,[.,[[.,.],.]]],.]] [1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>[.,[[.,[.,[.,[.,.]]]],.]] [1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]] [1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,6,5]=>[2,1,3,4,6,5]=>[[.,.],[.,[.,[[.,.],.]]]] [1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]=>[[.,.],[.,[[.,.],[.,.]]]] [1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3,5,6,4]=>[2,1,3,6,5,4]=>[[.,.],[.,[[[.,.],.],.]]] [1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,4,5]=>[2,1,3,5,6,4]=>[[.,.],[.,[[.,[.,.]],.]]] [1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]=>[[.,.],[[.,.],[.,[.,.]]]] [1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>[[.,.],[[.,.],[[.,.],.]]] [1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>[2,1,5,4,3,6]=>[[.,.],[[[.,.],.],[.,.]]] [1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,6,3]=>[2,1,6,4,5,3]=>[[.,.],[[[.,.],[.,.]],.]] [1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,3,5]=>[2,1,5,4,6,3]=>[[.,.],[[[.,.],[.,.]],.]] [1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,3,4,6]=>[2,1,4,5,3,6]=>[[.,.],[[.,[.,.]],[.,.]]] [1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,3,6,4]=>[2,1,5,6,3,4]=>[[.,.],[[.,[.,.]],[.,.]]] [1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,5,6,3,4]=>[2,1,4,6,5,3]=>[[.,.],[[.,[[.,.],.]],.]] [1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,3,4,5]=>[2,1,4,5,6,3]=>[[.,.],[[.,[.,[.,.]]],.]] [1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,4,5,6]=>[3,2,1,4,5,6]=>[[[.,.],.],[.,[.,[.,.]]]] [1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,5]=>[3,2,1,4,6,5]=>[[[.,.],.],[.,[[.,.],.]]] [1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,6]=>[3,2,1,5,4,6]=>[[[.,.],.],[[.,.],[.,.]]] [1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,6,4]=>[3,2,1,6,5,4]=>[[[.,.],.],[[[.,.],.],.]] [1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,6,4,5]=>[3,2,1,5,6,4]=>[[[.,.],.],[[.,[.,.]],.]] [1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,1,5,6]=>[4,2,3,1,5,6]=>[[[.,.],[.,.]],[.,[.,.]]] [1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,1,6,5]=>[4,2,3,1,6,5]=>[[[.,.],[.,.]],[[.,.],.]] [1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,1,6]=>[5,2,3,4,1,6]=>[[[.,.],[.,[.,.]]],[.,.]] [1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>[6,2,3,4,5,1]=>[[[.,.],[.,[.,[.,.]]]],.] [1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,1,5]=>[5,2,3,4,6,1]=>[[[.,.],[.,[.,[.,.]]]],.] [1,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,5,1,4,6]=>[4,2,3,5,1,6]=>[[[.,.],[.,[.,.]]],[.,.]] [1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,1,6,4]=>[5,2,3,6,1,4]=>[[[.,.],[.,[.,.]]],[.,.]] [1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,6,1,4]=>[4,2,3,6,5,1]=>[[[.,.],[.,[[.,.],.]]],.] [1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,1,4,5]=>[4,2,3,5,6,1]=>[[[.,.],[.,[.,[.,.]]]],.] [1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,1,3,5,6]=>[3,2,4,1,5,6]=>[[[.,.],[.,.]],[.,[.,.]]] [1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,1,3,6,5]=>[3,2,4,1,6,5]=>[[[.,.],[.,.]],[[.,.],.]] [1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,1,5,3,6]=>[4,2,5,1,3,6]=>[[[.,.],[.,.]],[.,[.,.]]] [1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,1,5,6,3]=>[4,2,6,1,5,3]=>[[[.,.],[.,.]],[[.,.],.]] [1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,1,6,3,5]=>[4,2,5,1,6,3]=>[[[.,.],[.,.]],[[.,.],.]] [1,1,0,1,1,0,1,0,0,0,1,0]=>[2,4,5,1,3,6]=>[3,2,5,4,1,6]=>[[[.,.],[[.,.],.]],[.,.]] [1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,5,1,6,3]=>[5,2,6,4,1,3]=>[[[.,.],[[.,.],.]],[.,.]] [1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,5,6,1,3]=>[3,2,6,4,5,1]=>[[[.,.],[[.,.],[.,.]]],.] [1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,6,1,3,5]=>[3,2,5,4,6,1]=>[[[.,.],[[.,.],[.,.]]],.] [1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,1,3,4,6]=>[3,2,4,5,1,6]=>[[[.,.],[.,[.,.]]],[.,.]] [1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,1,3,6,4]=>[3,2,5,6,1,4]=>[[[.,.],[.,[.,.]]],[.,.]] [1,1,0,1,1,1,0,0,1,0,0,0]=>[2,5,1,6,3,4]=>[5,2,4,6,1,3]=>[[[.,.],[.,[.,.]]],[.,.]] [1,1,0,1,1,1,0,1,0,0,0,0]=>[2,5,6,1,3,4]=>[3,2,4,6,5,1]=>[[[.,.],[.,[[.,.],.]]],.] [1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,1,3,4,5]=>[3,2,4,5,6,1]=>[[[.,.],[.,[.,[.,.]]]],.] [1,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,2,4,5,6]=>[2,3,1,4,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]] [1,1,1,0,0,0,1,0,1,1,0,0]=>[3,1,2,4,6,5]=>[2,3,1,4,6,5]=>[[.,[.,.]],[.,[[.,.],.]]] [1,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,2,5,4,6]=>[2,3,1,5,4,6]=>[[.,[.,.]],[[.,.],[.,.]]] [1,1,1,0,0,0,1,1,0,1,0,0]=>[3,1,2,5,6,4]=>[2,3,1,6,5,4]=>[[.,[.,.]],[[[.,.],.],.]] [1,1,1,0,0,0,1,1,1,0,0,0]=>[3,1,2,6,4,5]=>[2,3,1,5,6,4]=>[[.,[.,.]],[[.,[.,.]],.]] [1,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,4,2,5,6]=>[3,4,1,2,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]] [1,1,1,0,0,1,0,0,1,1,0,0]=>[3,1,4,2,6,5]=>[3,4,1,2,6,5]=>[[.,[.,.]],[.,[[.,.],.]]] [1,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,4,5,2,6]=>[3,5,1,4,2,6]=>[[.,[.,.]],[[.,.],[.,.]]] [1,1,1,0,0,1,0,1,0,1,0,0]=>[3,1,4,5,6,2]=>[3,6,1,4,5,2]=>[[.,[.,.]],[[.,[.,.]],.]] [1,1,1,0,0,1,0,1,1,0,0,0]=>[3,1,4,6,2,5]=>[3,5,1,4,6,2]=>[[.,[.,.]],[[.,[.,.]],.]] [1,1,1,0,0,1,1,0,0,0,1,0]=>[3,1,5,2,4,6]=>[3,4,1,5,2,6]=>[[.,[.,.]],[[.,.],[.,.]]] [1,1,1,0,0,1,1,0,0,1,0,0]=>[3,1,5,2,6,4]=>[3,5,1,6,2,4]=>[[.,[.,.]],[[.,.],[.,.]]] [1,1,1,0,0,1,1,0,1,0,0,0]=>[3,1,5,6,2,4]=>[3,4,1,6,5,2]=>[[.,[.,.]],[[[.,.],.],.]] [1,1,1,0,0,1,1,1,0,0,0,0]=>[3,1,6,2,4,5]=>[3,4,1,5,6,2]=>[[.,[.,.]],[[.,[.,.]],.]] [1,1,1,0,1,0,0,0,1,0,1,0]=>[3,4,1,2,5,6]=>[2,4,3,1,5,6]=>[[.,[[.,.],.]],[.,[.,.]]] [1,1,1,0,1,0,0,0,1,1,0,0]=>[3,4,1,2,6,5]=>[2,4,3,1,6,5]=>[[.,[[.,.],.]],[[.,.],.]] [1,1,1,0,1,0,0,1,0,0,1,0]=>[3,4,1,5,2,6]=>[4,5,3,1,2,6]=>[[[.,[.,.]],.],[.,[.,.]]] [1,1,1,0,1,0,0,1,0,1,0,0]=>[3,4,1,5,6,2]=>[4,6,3,1,5,2]=>[[[.,[.,.]],.],[[.,.],.]] [1,1,1,0,1,0,0,1,1,0,0,0]=>[3,4,1,6,2,5]=>[4,5,3,1,6,2]=>[[[.,[.,.]],.],[[.,.],.]] [1,1,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,1,2,6]=>[2,5,3,4,1,6]=>[[.,[[.,.],[.,.]]],[.,.]] [1,1,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,1,6,2]=>[5,6,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,.]] [1,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,1,2]=>[2,6,3,4,5,1]=>[[.,[[.,.],[.,[.,.]]]],.] [1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,6,1,2,5]=>[2,5,3,4,6,1]=>[[.,[[.,.],[.,[.,.]]]],.] [1,1,1,0,1,1,0,0,0,0,1,0]=>[3,5,1,2,4,6]=>[2,4,3,5,1,6]=>[[.,[[.,.],[.,.]]],[.,.]] [1,1,1,0,1,1,0,0,0,1,0,0]=>[3,5,1,2,6,4]=>[2,5,3,6,1,4]=>[[.,[[.,.],[.,.]]],[.,.]] [1,1,1,0,1,1,0,0,1,0,0,0]=>[3,5,1,6,2,4]=>[5,4,3,6,1,2]=>[[[[.,.],.],[.,.]],[.,.]] [1,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,6,1,2,4]=>[2,4,3,6,5,1]=>[[.,[[.,.],[[.,.],.]]],.] [1,1,1,0,1,1,1,0,0,0,0,0]=>[3,6,1,2,4,5]=>[2,4,3,5,6,1]=>[[.,[[.,.],[.,[.,.]]]],.] [1,1,1,1,0,0,0,0,1,0,1,0]=>[4,1,2,3,5,6]=>[2,3,4,1,5,6]=>[[.,[.,[.,.]]],[.,[.,.]]] [1,1,1,1,0,0,0,0,1,1,0,0]=>[4,1,2,3,6,5]=>[2,3,4,1,6,5]=>[[.,[.,[.,.]]],[[.,.],.]] [1,1,1,1,0,0,0,1,0,0,1,0]=>[4,1,2,5,3,6]=>[2,4,5,1,3,6]=>[[.,[.,[.,.]]],[.,[.,.]]] [1,1,1,1,0,0,0,1,0,1,0,0]=>[4,1,2,5,6,3]=>[2,4,6,1,5,3]=>[[.,[.,[.,.]]],[[.,.],.]] [1,1,1,1,0,0,0,1,1,0,0,0]=>[4,1,2,6,3,5]=>[2,4,5,1,6,3]=>[[.,[.,[.,.]]],[[.,.],.]] [1,1,1,1,0,0,1,0,0,0,1,0]=>[4,1,5,2,3,6]=>[4,3,5,1,2,6]=>[[[.,.],[.,.]],[.,[.,.]]] [1,1,1,1,0,0,1,0,0,1,0,0]=>[4,1,5,2,6,3]=>[4,5,6,1,2,3]=>[[.,[.,[.,.]]],[.,[.,.]]] [1,1,1,1,0,0,1,0,1,0,0,0]=>[4,1,5,6,2,3]=>[4,3,6,1,5,2]=>[[[.,.],[.,.]],[[.,.],.]] [1,1,1,1,0,0,1,1,0,0,0,0]=>[4,1,6,2,3,5]=>[4,3,5,1,6,2]=>[[[.,.],[.,.]],[[.,.],.]] [1,1,1,1,0,1,0,0,0,0,1,0]=>[4,5,1,2,3,6]=>[2,3,5,4,1,6]=>[[.,[.,[[.,.],.]]],[.,.]] [1,1,1,1,0,1,0,0,0,1,0,0]=>[4,5,1,2,6,3]=>[2,5,6,4,1,3]=>[[.,[[.,[.,.]],.]],[.,.]] [1,1,1,1,0,1,0,0,1,0,0,0]=>[4,5,1,6,2,3]=>[5,3,6,4,1,2]=>[[[.,.],[[.,.],.]],[.,.]] [1,1,1,1,0,1,0,1,0,0,0,0]=>[4,5,6,1,2,3]=>[2,3,6,4,5,1]=>[[.,[.,[[.,.],[.,.]]]],.] [1,1,1,1,0,1,1,0,0,0,0,0]=>[4,6,1,2,3,5]=>[2,3,5,4,6,1]=>[[.,[.,[[.,.],[.,.]]]],.] [1,1,1,1,1,0,0,0,0,0,1,0]=>[5,1,2,3,4,6]=>[2,3,4,5,1,6]=>[[.,[.,[.,[.,.]]]],[.,.]] [1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,2,3,6,4]=>[2,3,5,6,1,4]=>[[.,[.,[.,[.,.]]]],[.,.]] [1,1,1,1,1,0,0,0,1,0,0,0]=>[5,1,2,6,3,4]=>[2,5,4,6,1,3]=>[[.,[[.,.],[.,.]]],[.,.]] [1,1,1,1,1,0,0,1,0,0,0,0]=>[5,1,6,2,3,4]=>[5,3,4,6,1,2]=>[[[.,.],[.,[.,.]]],[.,.]] [1,1,1,1,1,0,1,0,0,0,0,0]=>[5,6,1,2,3,4]=>[2,3,4,6,5,1]=>[[.,[.,[.,[[.,.],.]]]],.] [1,1,1,1,1,1,0,0,0,0,0,0]=>[6,1,2,3,4,5]=>[2,3,4,5,6,1]=>[[.,[.,[.,[.,[.,.]]]]],.] [1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]] [1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]] [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]] [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,6,7,5]=>[1,2,3,4,7,6,5]=>[.,[.,[.,[.,[[[.,.],.],.]]]]] [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,7,5,6]=>[1,2,3,4,6,7,5]=>[.,[.,[.,[.,[[.,[.,.]],.]]]]] [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]] [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>[.,[.,[.,[[.,.],[[.,.],.]]]]] [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,6,4,7]=>[1,2,3,6,5,4,7]=>[.,[.,[.,[[[.,.],.],[.,.]]]]] [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,4]=>[1,2,3,7,5,6,4]=>[.,[.,[.,[[[.,.],[.,.]],.]]]] [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,4,6]=>[1,2,3,6,5,7,4]=>[.,[.,[.,[[[.,.],[.,.]],.]]]] [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,6,4,5,7]=>[1,2,3,5,6,4,7]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]] [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,6,4,7,5]=>[1,2,3,6,7,4,5]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]] [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,6,7,4,5]=>[1,2,3,5,7,6,4]=>[.,[.,[.,[[.,[[.,.],.]],.]]]] [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>[.,[.,[.,[[.,[.,[.,.]]],.]]]] [1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]] [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>[.,[.,[[.,.],[.,[[.,.],.]]]]] [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>[.,[.,[[.,.],[[.,.],[.,.]]]]] [1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,3,6,7,5]=>[1,2,4,3,7,6,5]=>[.,[.,[[.,.],[[[.,.],.],.]]]] [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,7,5,6]=>[1,2,4,3,6,7,5]=>[.,[.,[[.,.],[[.,[.,.]],.]]]] [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,3,6,7]=>[1,2,5,4,3,6,7]=>[.,[.,[[[.,.],.],[.,[.,.]]]]] [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,3,7,6]=>[1,2,5,4,3,7,6]=>[.,[.,[[[.,.],.],[[.,.],.]]]] [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,3,7]=>[1,2,6,4,5,3,7]=>[.,[.,[[[.,.],[.,.]],[.,.]]]] [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,3]=>[1,2,7,4,5,6,3]=>[.,[.,[[[.,.],[.,[.,.]]],.]]] [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,7,3,6]=>[1,2,6,4,5,7,3]=>[.,[.,[[[.,.],[.,[.,.]]],.]]] [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,6,3,5,7]=>[1,2,5,4,6,3,7]=>[.,[.,[[[.,.],[.,.]],[.,.]]]] [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,4,6,3,7,5]=>[1,2,6,4,7,3,5]=>[.,[.,[[[.,.],[.,.]],[.,.]]]] [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,6,7,3,5]=>[1,2,5,4,7,6,3]=>[.,[.,[[[.,.],[[.,.],.]],.]]] [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,7,3,5,6]=>[1,2,5,4,6,7,3]=>[.,[.,[[[.,.],[.,[.,.]]],.]]] [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,5,3,4,6,7]=>[1,2,4,5,3,6,7]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]] [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,5,3,4,7,6]=>[1,2,4,5,3,7,6]=>[.,[.,[[.,[.,.]],[[.,.],.]]]] [1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,5,3,6,4,7]=>[1,2,5,6,3,4,7]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]] [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,5,3,6,7,4]=>[1,2,5,7,3,6,4]=>[.,[.,[[.,[.,.]],[[.,.],.]]]] [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,5,3,7,4,6]=>[1,2,5,6,3,7,4]=>[.,[.,[[.,[.,.]],[[.,.],.]]]] [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,5,6,3,4,7]=>[1,2,4,6,5,3,7]=>[.,[.,[[.,[[.,.],.]],[.,.]]]] [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,5,6,3,7,4]=>[1,2,6,7,5,3,4]=>[.,[.,[[[.,[.,.]],.],[.,.]]]] [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,3,4]=>[1,2,4,7,5,6,3]=>[.,[.,[[.,[[.,.],[.,.]]],.]]] [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,5,7,3,4,6]=>[1,2,4,6,5,7,3]=>[.,[.,[[.,[[.,.],[.,.]]],.]]] [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]] [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,6,3,4,7,5]=>[1,2,4,6,7,3,5]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]] [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,6,3,7,4,5]=>[1,2,6,5,7,3,4]=>[.,[.,[[[.,.],[.,.]],[.,.]]]] [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,6,7,3,4,5]=>[1,2,4,5,7,6,3]=>[.,[.,[[.,[.,[[.,.],.]]],.]]] [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>[.,[.,[[.,[.,[.,[.,.]]]],.]]] [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]] [1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>[.,[[.,.],[.,[.,[[.,.],.]]]]] [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]] [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,6,7,5]=>[1,3,2,4,7,6,5]=>[.,[[.,.],[.,[[[.,.],.],.]]]] [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,7,5,6]=>[1,3,2,4,6,7,5]=>[.,[[.,.],[.,[[.,[.,.]],.]]]] [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]] [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]=>[.,[[.,.],[[.,.],[[.,.],.]]]] [1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,5,6,4,7]=>[1,3,2,6,5,4,7]=>[.,[[.,.],[[[.,.],.],[.,.]]]] [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,4]=>[1,3,2,7,5,6,4]=>[.,[[.,.],[[[.,.],[.,.]],.]]] [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,4,6]=>[1,3,2,6,5,7,4]=>[.,[[.,.],[[[.,.],[.,.]],.]]] [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,6,4,5,7]=>[1,3,2,5,6,4,7]=>[.,[[.,.],[[.,[.,.]],[.,.]]]] [1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,4,7,5]=>[1,3,2,6,7,4,5]=>[.,[[.,.],[[.,[.,.]],[.,.]]]] [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,6,7,4,5]=>[1,3,2,5,7,6,4]=>[.,[[.,.],[[.,[[.,.],.]],.]]] [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,7,4,5,6]=>[1,3,2,5,6,7,4]=>[.,[[.,.],[[.,[.,[.,.]]],.]]] [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7]=>[1,4,3,2,5,6,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]] [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5,7,6]=>[1,4,3,2,5,7,6]=>[.,[[[.,.],.],[.,[[.,.],.]]]] [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,7]=>[1,4,3,2,6,5,7]=>[.,[[[.,.],.],[[.,.],[.,.]]]] [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,2,6,7,5]=>[1,4,3,2,7,6,5]=>[.,[[[.,.],.],[[[.,.],.],.]]] [1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,2,7,5,6]=>[1,4,3,2,6,7,5]=>[.,[[[.,.],.],[[.,[.,.]],.]]] [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,2,6,7]=>[1,5,3,4,2,6,7]=>[.,[[[.,.],[.,.]],[.,[.,.]]]] [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6]=>[1,5,3,4,2,7,6]=>[.,[[[.,.],[.,.]],[[.,.],.]]] [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,2,7]=>[1,6,3,4,5,2,7]=>[.,[[[.,.],[.,[.,.]]],[.,.]]] [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,2]=>[1,7,3,4,5,6,2]=>[.,[[[.,.],[.,[.,[.,.]]]],.]] [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,7,2,6]=>[1,6,3,4,5,7,2]=>[.,[[[.,.],[.,[.,[.,.]]]],.]] [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,2,5,7]=>[1,5,3,4,6,2,7]=>[.,[[[.,.],[.,[.,.]]],[.,.]]] [1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,6,2,7,5]=>[1,6,3,4,7,2,5]=>[.,[[[.,.],[.,[.,.]]],[.,.]]] [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,6,7,2,5]=>[1,5,3,4,7,6,2]=>[.,[[[.,.],[.,[[.,.],.]]],.]] [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,7,2,5,6]=>[1,5,3,4,6,7,2]=>[.,[[[.,.],[.,[.,[.,.]]]],.]] [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,5,2,4,6,7]=>[1,4,3,5,2,6,7]=>[.,[[[.,.],[.,.]],[.,[.,.]]]] [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,2,4,7,6]=>[1,4,3,5,2,7,6]=>[.,[[[.,.],[.,.]],[[.,.],.]]] [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,5,2,6,4,7]=>[1,5,3,6,2,4,7]=>[.,[[[.,.],[.,.]],[.,[.,.]]]] [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,2,6,7,4]=>[1,5,3,7,2,6,4]=>[.,[[[.,.],[.,.]],[[.,.],.]]] [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,2,7,4,6]=>[1,5,3,6,2,7,4]=>[.,[[[.,.],[.,.]],[[.,.],.]]] [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,5,6,2,4,7]=>[1,4,3,6,5,2,7]=>[.,[[[.,.],[[.,.],.]],[.,.]]] [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,5,6,2,7,4]=>[1,6,3,7,5,2,4]=>[.,[[[.,.],[[.,.],.]],[.,.]]] [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,2,4]=>[1,4,3,7,5,6,2]=>[.,[[[.,.],[[.,.],[.,.]]],.]] [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,7,2,4,6]=>[1,4,3,6,5,7,2]=>[.,[[[.,.],[[.,.],[.,.]]],.]] [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,6,2,4,5,7]=>[1,4,3,5,6,2,7]=>[.,[[[.,.],[.,[.,.]]],[.,.]]] [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,6,2,4,7,5]=>[1,4,3,6,7,2,5]=>[.,[[[.,.],[.,[.,.]]],[.,.]]] [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,6,2,7,4,5]=>[1,6,3,5,7,2,4]=>[.,[[[.,.],[.,[.,.]]],[.,.]]] [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,6,7,2,4,5]=>[1,4,3,5,7,6,2]=>[.,[[[.,.],[.,[[.,.],.]]],.]] [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>[.,[[[.,.],[.,[.,[.,.]]]],.]] [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,2,3,5,6,7]=>[1,3,4,2,5,6,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]] [1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,2,3,5,7,6]=>[1,3,4,2,5,7,6]=>[.,[[.,[.,.]],[.,[[.,.],.]]]] [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,2,3,6,5,7]=>[1,3,4,2,6,5,7]=>[.,[[.,[.,.]],[[.,.],[.,.]]]] [1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,2,3,6,7,5]=>[1,3,4,2,7,6,5]=>[.,[[.,[.,.]],[[[.,.],.],.]]] [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,2,3,7,5,6]=>[1,3,4,2,6,7,5]=>[.,[[.,[.,.]],[[.,[.,.]],.]]] [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,2,5,3,6,7]=>[1,4,5,2,3,6,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]] [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,2,5,3,7,6]=>[1,4,5,2,3,7,6]=>[.,[[.,[.,.]],[.,[[.,.],.]]]] [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,2,5,6,3,7]=>[1,4,6,2,5,3,7]=>[.,[[.,[.,.]],[[.,.],[.,.]]]] [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,5,6,7,3]=>[1,4,7,2,5,6,3]=>[.,[[.,[.,.]],[[.,[.,.]],.]]] [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,2,5,7,3,6]=>[1,4,6,2,5,7,3]=>[.,[[.,[.,.]],[[.,[.,.]],.]]] [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,2,6,3,5,7]=>[1,4,5,2,6,3,7]=>[.,[[.,[.,.]],[[.,.],[.,.]]]] [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,6,3,7,5]=>[1,4,6,2,7,3,5]=>[.,[[.,[.,.]],[[.,.],[.,.]]]] [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,2,6,7,3,5]=>[1,4,5,2,7,6,3]=>[.,[[.,[.,.]],[[[.,.],.],.]]] [1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>[.,[[.,[.,.]],[[.,[.,.]],.]]] [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,4,5,2,3,6,7]=>[1,3,5,4,2,6,7]=>[.,[[.,[[.,.],.]],[.,[.,.]]]] [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,4,5,2,3,7,6]=>[1,3,5,4,2,7,6]=>[.,[[.,[[.,.],.]],[[.,.],.]]] [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,4,5,2,6,3,7]=>[1,5,6,4,2,3,7]=>[.,[[[.,[.,.]],.],[.,[.,.]]]] [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,5,2,6,7,3]=>[1,5,7,4,2,6,3]=>[.,[[[.,[.,.]],.],[[.,.],.]]] [1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,5,2,7,3,6]=>[1,5,6,4,2,7,3]=>[.,[[[.,[.,.]],.],[[.,.],.]]] [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,4,5,6,2,3,7]=>[1,3,6,4,5,2,7]=>[.,[[.,[[.,.],[.,.]]],[.,.]]] [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,5,6,2,7,3]=>[1,6,7,4,5,2,3]=>[.,[[[.,[.,.]],[.,.]],[.,.]]] [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,2,3]=>[1,3,7,4,5,6,2]=>[.,[[.,[[.,.],[.,[.,.]]]],.]] [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,4,5,7,2,3,6]=>[1,3,6,4,5,7,2]=>[.,[[.,[[.,.],[.,[.,.]]]],.]] [1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,4,6,2,3,5,7]=>[1,3,5,4,6,2,7]=>[.,[[.,[[.,.],[.,.]]],[.,.]]] [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,6,2,3,7,5]=>[1,3,6,4,7,2,5]=>[.,[[.,[[.,.],[.,.]]],[.,.]]] [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,4,6,2,7,3,5]=>[1,6,5,4,7,2,3]=>[.,[[[[.,.],.],[.,.]],[.,.]]] [1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,4,6,7,2,3,5]=>[1,3,5,4,7,6,2]=>[.,[[.,[[.,.],[[.,.],.]]],.]] [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>[.,[[.,[[.,.],[.,[.,.]]]],.]] [1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]] [1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,5,2,3,4,7,6]=>[1,3,4,5,2,7,6]=>[.,[[.,[.,[.,.]]],[[.,.],.]]] [1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,5,2,3,6,4,7]=>[1,3,5,6,2,4,7]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]] [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,2,3,6,7,4]=>[1,3,5,7,2,6,4]=>[.,[[.,[.,[.,.]]],[[.,.],.]]] [1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>[.,[[.,[.,[.,.]]],[[.,.],.]]] [1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,5,2,6,3,4,7]=>[1,5,4,6,2,3,7]=>[.,[[[.,.],[.,.]],[.,[.,.]]]] [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,2,6,3,7,4]=>[1,5,6,7,2,3,4]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]] [1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,5,2,6,7,3,4]=>[1,5,4,7,2,6,3]=>[.,[[[.,.],[.,.]],[[.,.],.]]] [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>[.,[[[.,.],[.,.]],[[.,.],.]]] [1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,5,6,2,3,4,7]=>[1,3,4,6,5,2,7]=>[.,[[.,[.,[[.,.],.]]],[.,.]]] [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,5,6,2,3,7,4]=>[1,3,6,7,5,2,4]=>[.,[[.,[[.,[.,.]],.]],[.,.]]] [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,5,6,2,7,3,4]=>[1,6,4,7,5,2,3]=>[.,[[[.,.],[[.,.],.]],[.,.]]] [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,2,3,4]=>[1,3,4,7,5,6,2]=>[.,[[.,[.,[[.,.],[.,.]]]],.]] [1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>[.,[[.,[.,[[.,.],[.,.]]]],.]] [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]] [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]] [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>[.,[[.,[[.,.],[.,.]]],[.,.]]] [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>[.,[[[.,.],[.,[.,.]]],[.,.]]] [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>[.,[[.,[.,[.,[[.,.],.]]]],.]] [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>[.,[[.,[.,[.,[.,[.,.]]]]],.]] [1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]] [1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]] [1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,6,7,5]=>[2,1,3,4,7,6,5]=>[[.,.],[.,[.,[[[.,.],.],.]]]] [1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,7,5,6]=>[2,1,3,4,6,7,5]=>[[.,.],[.,[.,[[.,[.,.]],.]]]] [1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]] [1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]] [1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,6,4,7]=>[2,1,3,6,5,4,7]=>[[.,.],[.,[[[.,.],.],[.,.]]]] [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,4]=>[2,1,3,7,5,6,4]=>[[.,.],[.,[[[.,.],[.,.]],.]]] [1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,3,5,7,4,6]=>[2,1,3,6,5,7,4]=>[[.,.],[.,[[[.,.],[.,.]],.]]] [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,6,4,5,7]=>[2,1,3,5,6,4,7]=>[[.,.],[.,[[.,[.,.]],[.,.]]]] [1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,6,4,7,5]=>[2,1,3,6,7,4,5]=>[[.,.],[.,[[.,[.,.]],[.,.]]]] [1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,6,7,4,5]=>[2,1,3,5,7,6,4]=>[[.,.],[.,[[.,[[.,.],.]],.]]] [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,7,4,5,6]=>[2,1,3,5,6,7,4]=>[[.,.],[.,[[.,[.,[.,.]]],.]]] [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]] [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]] [1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,3,6,7,5]=>[2,1,4,3,7,6,5]=>[[.,.],[[.,.],[[[.,.],.],.]]] [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,7,5,6]=>[2,1,4,3,6,7,5]=>[[.,.],[[.,.],[[.,[.,.]],.]]] [1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,5,3,6,7]=>[2,1,5,4,3,6,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]] [1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,3,7,6]=>[2,1,5,4,3,7,6]=>[[.,.],[[[.,.],.],[[.,.],.]]] [1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,6,3,7]=>[2,1,6,4,5,3,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]] [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,3]=>[2,1,7,4,5,6,3]=>[[.,.],[[[.,.],[.,[.,.]]],.]] [1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,7,3,6]=>[2,1,6,4,5,7,3]=>[[.,.],[[[.,.],[.,[.,.]]],.]] [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,6,3,5,7]=>[2,1,5,4,6,3,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]] [1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,4,6,3,7,5]=>[2,1,6,4,7,3,5]=>[[.,.],[[[.,.],[.,.]],[.,.]]] [1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,4,6,7,3,5]=>[2,1,5,4,7,6,3]=>[[.,.],[[[.,.],[[.,.],.]],.]] [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,4,7,3,5,6]=>[2,1,5,4,6,7,3]=>[[.,.],[[[.,.],[.,[.,.]]],.]] [1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,3,4,6,7]=>[2,1,4,5,3,6,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]] [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,5,3,4,7,6]=>[2,1,4,5,3,7,6]=>[[.,.],[[.,[.,.]],[[.,.],.]]] [1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,3,6,4,7]=>[2,1,5,6,3,4,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]] [1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,3,6,7,4]=>[2,1,5,7,3,6,4]=>[[.,.],[[.,[.,.]],[[.,.],.]]] [1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,3,7,4,6]=>[2,1,5,6,3,7,4]=>[[.,.],[[.,[.,.]],[[.,.],.]]] [1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,5,6,3,4,7]=>[2,1,4,6,5,3,7]=>[[.,.],[[.,[[.,.],.]],[.,.]]] [1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,5,6,3,7,4]=>[2,1,6,7,5,3,4]=>[[.,.],[[[.,[.,.]],.],[.,.]]] [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,5,6,7,3,4]=>[2,1,4,7,5,6,3]=>[[.,.],[[.,[[.,.],[.,.]]],.]] [1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,5,7,3,4,6]=>[2,1,4,6,5,7,3]=>[[.,.],[[.,[[.,.],[.,.]]],.]] [1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,6,3,4,5,7]=>[2,1,4,5,6,3,7]=>[[.,.],[[.,[.,[.,.]]],[.,.]]] [1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,6,3,4,7,5]=>[2,1,4,6,7,3,5]=>[[.,.],[[.,[.,[.,.]]],[.,.]]] [1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,6,3,7,4,5]=>[2,1,6,5,7,3,4]=>[[.,.],[[[.,.],[.,.]],[.,.]]] [1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,6,7,3,4,5]=>[2,1,4,5,7,6,3]=>[[.,.],[[.,[.,[[.,.],.]]],.]] [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,7,3,4,5,6]=>[2,1,4,5,6,7,3]=>[[.,.],[[.,[.,[.,[.,.]]]],.]] [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,7,6]=>[3,2,1,4,5,7,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]] [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,1,4,6,5,7]=>[3,2,1,4,6,5,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]] [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,6,7,5]=>[3,2,1,4,7,6,5]=>[[[.,.],.],[.,[[[.,.],.],.]]] [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,7,5,6]=>[3,2,1,4,6,7,5]=>[[[.,.],.],[.,[[.,[.,.]],.]]] [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,4,6,7]=>[3,2,1,5,4,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]] [1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6]=>[3,2,1,5,4,7,6]=>[[[.,.],.],[[.,.],[[.,.],.]]] [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,1,5,6,4,7]=>[3,2,1,6,5,4,7]=>[[[.,.],.],[[[.,.],.],[.,.]]] [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,4]=>[3,2,1,7,5,6,4]=>[[[.,.],.],[[[.,.],[.,.]],.]] [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,1,5,7,4,6]=>[3,2,1,6,5,7,4]=>[[[.,.],.],[[[.,.],[.,.]],.]] [1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1,6,4,5,7]=>[3,2,1,5,6,4,7]=>[[[.,.],.],[[.,[.,.]],[.,.]]] [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,4,7,5]=>[3,2,1,6,7,4,5]=>[[[.,.],.],[[.,[.,.]],[.,.]]] [1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1,6,7,4,5]=>[3,2,1,5,7,6,4]=>[[[.,.],.],[[.,[[.,.],.]],.]] [1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,7,4,5,6]=>[3,2,1,5,6,7,4]=>[[[.,.],.],[[.,[.,[.,.]]],.]] [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7]=>[4,2,3,1,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,5,7,6]=>[4,2,3,1,5,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]] [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,7]=>[4,2,3,1,6,5,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]] [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,1,6,7,5]=>[4,2,3,1,7,6,5]=>[[[.,.],[.,.]],[[[.,.],.],.]] [1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,7,5,6]=>[4,2,3,1,6,7,5]=>[[[.,.],[.,.]],[[.,[.,.]],.]] [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,1,6,7]=>[5,2,3,4,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6]=>[5,2,3,4,1,7,6]=>[[[.,.],[.,[.,.]]],[[.,.],.]] [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,1,7]=>[6,2,3,4,5,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,1]=>[7,2,3,4,5,6,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.] [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,7,1,6]=>[6,2,3,4,5,7,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.] [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,6,1,5,7]=>[5,2,3,4,6,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,6,1,7,5]=>[6,2,3,4,7,1,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,6,7,1,5]=>[5,2,3,4,7,6,1]=>[[[.,.],[.,[.,[[.,.],.]]]],.] [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,7,1,5,6]=>[5,2,3,4,6,7,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.] [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,5,1,4,6,7]=>[4,2,3,5,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,3,5,1,4,7,6]=>[4,2,3,5,1,7,6]=>[[[.,.],[.,[.,.]]],[[.,.],.]] [1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,5,1,6,4,7]=>[5,2,3,6,1,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,5,1,6,7,4]=>[5,2,3,7,1,6,4]=>[[[.,.],[.,[.,.]]],[[.,.],.]] [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,1,7,4,6]=>[5,2,3,6,1,7,4]=>[[[.,.],[.,[.,.]]],[[.,.],.]] [1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,5,6,1,4,7]=>[4,2,3,6,5,1,7]=>[[[.,.],[.,[[.,.],.]]],[.,.]] [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,5,6,1,7,4]=>[6,2,3,7,5,1,4]=>[[[.,.],[.,[[.,.],.]]],[.,.]] [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,1,4]=>[4,2,3,7,5,6,1]=>[[[.,.],[.,[[.,.],[.,.]]]],.] [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,7,1,4,6]=>[4,2,3,6,5,7,1]=>[[[.,.],[.,[[.,.],[.,.]]]],.] [1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,6,1,4,5,7]=>[4,2,3,5,6,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,6,1,4,7,5]=>[4,2,3,6,7,1,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,6,1,7,4,5]=>[6,2,3,5,7,1,4]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,6,7,1,4,5]=>[4,2,3,5,7,6,1]=>[[[.,.],[.,[.,[[.,.],.]]]],.] [1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,7,1,4,5,6]=>[4,2,3,5,6,7,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.] [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,1,3,5,6,7]=>[3,2,4,1,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,1,3,5,7,6]=>[3,2,4,1,5,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]] [1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,1,3,6,5,7]=>[3,2,4,1,6,5,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]] [1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,1,3,6,7,5]=>[3,2,4,1,7,6,5]=>[[[.,.],[.,.]],[[[.,.],.],.]] [1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,1,3,7,5,6]=>[3,2,4,1,6,7,5]=>[[[.,.],[.,.]],[[.,[.,.]],.]] [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,1,5,3,6,7]=>[4,2,5,1,3,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,1,5,3,7,6]=>[4,2,5,1,3,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]] [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,4,1,5,6,3,7]=>[4,2,6,1,5,3,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]] [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,1,5,6,7,3]=>[4,2,7,1,5,6,3]=>[[[.,.],[.,.]],[[.,[.,.]],.]] [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,4,1,5,7,3,6]=>[4,2,6,1,5,7,3]=>[[[.,.],[.,.]],[[.,[.,.]],.]] [1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,1,6,3,5,7]=>[4,2,5,1,6,3,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]] [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,1,6,3,7,5]=>[4,2,6,1,7,3,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]] [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,1,6,7,3,5]=>[4,2,5,1,7,6,3]=>[[[.,.],[.,.]],[[[.,.],.],.]] [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,1,7,3,5,6]=>[4,2,5,1,6,7,3]=>[[[.,.],[.,.]],[[.,[.,.]],.]] [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,4,5,1,3,6,7]=>[3,2,5,4,1,6,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]] [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,4,5,1,3,7,6]=>[3,2,5,4,1,7,6]=>[[[.,.],[[.,.],.]],[[.,.],.]] [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,4,5,1,6,3,7]=>[5,2,6,4,1,3,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]] [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,4,5,1,6,7,3]=>[5,2,7,4,1,6,3]=>[[[.,.],[[.,.],.]],[[.,.],.]] [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,4,5,1,7,3,6]=>[5,2,6,4,1,7,3]=>[[[.,.],[[.,.],.]],[[.,.],.]] [1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,4,5,6,1,3,7]=>[3,2,6,4,5,1,7]=>[[[.,.],[[.,.],[.,.]]],[.,.]] [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,4,5,6,1,7,3]=>[6,2,7,4,5,1,3]=>[[[.,.],[[.,.],[.,.]]],[.,.]] [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,1,3]=>[3,2,7,4,5,6,1]=>[[[.,.],[[.,.],[.,[.,.]]]],.] [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,4,5,7,1,3,6]=>[3,2,6,4,5,7,1]=>[[[.,.],[[.,.],[.,[.,.]]]],.] [1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,4,6,1,3,5,7]=>[3,2,5,4,6,1,7]=>[[[.,.],[[.,.],[.,.]]],[.,.]] [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,4,6,1,3,7,5]=>[3,2,6,4,7,1,5]=>[[[.,.],[[.,.],[.,.]]],[.,.]] [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,4,6,1,7,3,5]=>[6,2,5,4,7,1,3]=>[[[.,.],[[.,.],[.,.]]],[.,.]] [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,4,6,7,1,3,5]=>[3,2,5,4,7,6,1]=>[[[.,.],[[.,.],[[.,.],.]]],.] [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,4,7,1,3,5,6]=>[3,2,5,4,6,7,1]=>[[[.,.],[[.,.],[.,[.,.]]]],.] [1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,5,1,3,4,6,7]=>[3,2,4,5,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,5,1,3,4,7,6]=>[3,2,4,5,1,7,6]=>[[[.,.],[.,[.,.]]],[[.,.],.]] [1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,5,1,3,6,4,7]=>[3,2,5,6,1,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,5,1,3,6,7,4]=>[3,2,5,7,1,6,4]=>[[[.,.],[.,[.,.]]],[[.,.],.]] [1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,5,1,3,7,4,6]=>[3,2,5,6,1,7,4]=>[[[.,.],[.,[.,.]]],[[.,.],.]] [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,5,1,6,3,4,7]=>[5,2,4,6,1,3,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,5,1,6,3,7,4]=>[5,2,6,7,1,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,5,1,6,7,3,4]=>[5,2,4,7,1,6,3]=>[[[.,.],[.,[.,.]]],[[.,.],.]] [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,5,1,7,3,4,6]=>[5,2,4,6,1,7,3]=>[[[.,.],[.,[.,.]]],[[.,.],.]] [1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,5,6,1,3,4,7]=>[3,2,4,6,5,1,7]=>[[[.,.],[.,[[.,.],.]]],[.,.]] [1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,5,6,1,3,7,4]=>[3,2,6,7,5,1,4]=>[[[.,.],[[.,[.,.]],.]],[.,.]] [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,5,6,1,7,3,4]=>[6,2,4,7,5,1,3]=>[[[.,.],[.,[[.,.],.]]],[.,.]] [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,1,3,4]=>[3,2,4,7,5,6,1]=>[[[.,.],[.,[[.,.],[.,.]]]],.] [1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,5,7,1,3,4,6]=>[3,2,4,6,5,7,1]=>[[[.,.],[.,[[.,.],[.,.]]]],.] [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,6,1,3,4,5,7]=>[3,2,4,5,6,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,6,1,3,4,7,5]=>[3,2,4,6,7,1,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,6,1,3,7,4,5]=>[3,2,6,5,7,1,4]=>[[[.,.],[[.,.],[.,.]]],[.,.]] [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,6,1,7,3,4,5]=>[6,2,4,5,7,1,3]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,6,7,1,3,4,5]=>[3,2,4,5,7,6,1]=>[[[.,.],[.,[.,[[.,.],.]]]],.] [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,7,1,3,4,5,6]=>[3,2,4,5,6,7,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.] [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,2,4,5,6,7]=>[2,3,1,4,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,1,2,4,5,7,6]=>[2,3,1,4,5,7,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]] [1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,1,2,4,6,5,7]=>[2,3,1,4,6,5,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]] [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,1,2,4,6,7,5]=>[2,3,1,4,7,6,5]=>[[.,[.,.]],[.,[[[.,.],.],.]]] [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,1,2,4,7,5,6]=>[2,3,1,4,6,7,5]=>[[.,[.,.]],[.,[[.,[.,.]],.]]] [1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,1,2,5,4,6,7]=>[2,3,1,5,4,6,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]] [1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,1,2,5,4,7,6]=>[2,3,1,5,4,7,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]] [1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,1,2,5,6,4,7]=>[2,3,1,6,5,4,7]=>[[.,[.,.]],[[[.,.],.],[.,.]]] [1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,1,2,5,6,7,4]=>[2,3,1,7,5,6,4]=>[[.,[.,.]],[[[.,.],[.,.]],.]] [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,1,2,5,7,4,6]=>[2,3,1,6,5,7,4]=>[[.,[.,.]],[[[.,.],[.,.]],.]] [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,1,2,6,4,5,7]=>[2,3,1,5,6,4,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]] [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,1,2,6,4,7,5]=>[2,3,1,6,7,4,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]] [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,1,2,6,7,4,5]=>[2,3,1,5,7,6,4]=>[[.,[.,.]],[[.,[[.,.],.]],.]] [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,1,2,7,4,5,6]=>[2,3,1,5,6,7,4]=>[[.,[.,.]],[[.,[.,[.,.]]],.]] [1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,1,4,2,5,6,7]=>[3,4,1,2,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,1,4,2,5,7,6]=>[3,4,1,2,5,7,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]] [1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,1,4,2,6,5,7]=>[3,4,1,2,6,5,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]] [1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,1,4,2,6,7,5]=>[3,4,1,2,7,6,5]=>[[.,[.,.]],[.,[[[.,.],.],.]]] [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,1,4,2,7,5,6]=>[3,4,1,2,6,7,5]=>[[.,[.,.]],[.,[[.,[.,.]],.]]] [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,1,4,5,2,6,7]=>[3,5,1,4,2,6,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]] [1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,1,4,5,2,7,6]=>[3,5,1,4,2,7,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]] [1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,1,4,5,6,2,7]=>[3,6,1,4,5,2,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]] [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,1,4,5,6,7,2]=>[3,7,1,4,5,6,2]=>[[.,[.,.]],[[.,[.,[.,.]]],.]] [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,1,4,5,7,2,6]=>[3,6,1,4,5,7,2]=>[[.,[.,.]],[[.,[.,[.,.]]],.]] [1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,1,4,6,2,5,7]=>[3,5,1,4,6,2,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]] [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,1,4,6,2,7,5]=>[3,6,1,4,7,2,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]] [1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,1,4,6,7,2,5]=>[3,5,1,4,7,6,2]=>[[.,[.,.]],[[.,[[.,.],.]],.]] [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,1,4,7,2,5,6]=>[3,5,1,4,6,7,2]=>[[.,[.,.]],[[.,[.,[.,.]]],.]] [1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,1,5,2,4,6,7]=>[3,4,1,5,2,6,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]] [1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,1,5,2,4,7,6]=>[3,4,1,5,2,7,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]] [1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,1,5,2,6,4,7]=>[3,5,1,6,2,4,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]] [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,1,5,2,6,7,4]=>[3,5,1,7,2,6,4]=>[[.,[.,.]],[[.,.],[[.,.],.]]] [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,1,5,2,7,4,6]=>[3,5,1,6,2,7,4]=>[[.,[.,.]],[[.,.],[[.,.],.]]] [1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,1,5,6,2,4,7]=>[3,4,1,6,5,2,7]=>[[.,[.,.]],[[[.,.],.],[.,.]]] [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,1,5,6,2,7,4]=>[3,6,1,7,5,2,4]=>[[.,[.,.]],[[[.,.],.],[.,.]]] [1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,1,5,6,7,2,4]=>[3,4,1,7,5,6,2]=>[[.,[.,.]],[[[.,.],[.,.]],.]] [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,1,5,7,2,4,6]=>[3,4,1,6,5,7,2]=>[[.,[.,.]],[[[.,.],[.,.]],.]] [1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,1,6,2,4,5,7]=>[3,4,1,5,6,2,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]] [1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,1,6,2,4,7,5]=>[3,4,1,6,7,2,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]] [1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,1,6,2,7,4,5]=>[3,6,1,5,7,2,4]=>[[.,[.,.]],[[.,[.,.]],[.,.]]] [1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,1,6,7,2,4,5]=>[3,4,1,5,7,6,2]=>[[.,[.,.]],[[.,[[.,.],.]],.]] [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,1,7,2,4,5,6]=>[3,4,1,5,6,7,2]=>[[.,[.,.]],[[.,[.,[.,.]]],.]] [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,4,1,2,5,6,7]=>[2,4,3,1,5,6,7]=>[[.,[[.,.],.]],[.,[.,[.,.]]]] [1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,4,1,2,5,7,6]=>[2,4,3,1,5,7,6]=>[[.,[[.,.],.]],[.,[[.,.],.]]] [1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,4,1,2,6,5,7]=>[2,4,3,1,6,5,7]=>[[.,[[.,.],.]],[[.,.],[.,.]]] [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,4,1,2,6,7,5]=>[2,4,3,1,7,6,5]=>[[.,[[.,.],.]],[[[.,.],.],.]] [1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,4,1,2,7,5,6]=>[2,4,3,1,6,7,5]=>[[.,[[.,.],.]],[[.,[.,.]],.]] [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,4,1,5,2,6,7]=>[4,5,3,1,2,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]] [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,4,1,5,2,7,6]=>[4,5,3,1,2,7,6]=>[[[.,[.,.]],.],[.,[[.,.],.]]] [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,4,1,5,6,2,7]=>[4,6,3,1,5,2,7]=>[[[.,[.,.]],.],[[.,.],[.,.]]] [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,1,5,6,7,2]=>[4,7,3,1,5,6,2]=>[[[.,[.,.]],.],[[.,[.,.]],.]] [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,4,1,5,7,2,6]=>[4,6,3,1,5,7,2]=>[[[.,[.,.]],.],[[.,[.,.]],.]] [1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,4,1,6,2,5,7]=>[4,5,3,1,6,2,7]=>[[[.,[.,.]],.],[[.,.],[.,.]]] [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,4,1,6,2,7,5]=>[4,6,3,1,7,2,5]=>[[[.,[.,.]],.],[[.,.],[.,.]]] [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,4,1,6,7,2,5]=>[4,5,3,1,7,6,2]=>[[[.,[.,.]],.],[[[.,.],.],.]] [1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,4,1,7,2,5,6]=>[4,5,3,1,6,7,2]=>[[[.,[.,.]],.],[[.,[.,.]],.]] [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,4,5,1,2,6,7]=>[2,5,3,4,1,6,7]=>[[.,[[.,.],[.,.]]],[.,[.,.]]] [1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,4,5,1,2,7,6]=>[2,5,3,4,1,7,6]=>[[.,[[.,.],[.,.]]],[[.,.],.]] [1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,4,5,1,6,2,7]=>[5,6,3,4,1,2,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]] [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,1,6,7,2]=>[5,7,3,4,1,6,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]] [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,4,5,1,7,2,6]=>[5,6,3,4,1,7,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]] [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,6,1,2,7]=>[2,6,3,4,5,1,7]=>[[.,[[.,.],[.,[.,.]]]],[.,.]] [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,1,7,2]=>[6,7,3,4,5,1,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]] [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,1,2]=>[2,7,3,4,5,6,1]=>[[.,[[.,.],[.,[.,[.,.]]]]],.] [1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,4,5,7,1,2,6]=>[2,6,3,4,5,7,1]=>[[.,[[.,.],[.,[.,[.,.]]]]],.] [1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,4,6,1,2,5,7]=>[2,5,3,4,6,1,7]=>[[.,[[.,.],[.,[.,.]]]],[.,.]] [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,4,6,1,2,7,5]=>[2,6,3,4,7,1,5]=>[[.,[[.,.],[.,[.,.]]]],[.,.]] [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,4,6,1,7,2,5]=>[6,5,3,4,7,1,2]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,4,6,7,1,2,5]=>[2,5,3,4,7,6,1]=>[[.,[[.,.],[.,[[.,.],.]]]],.] [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,7,1,2,5,6]=>[2,5,3,4,6,7,1]=>[[.,[[.,.],[.,[.,[.,.]]]]],.] [1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,5,1,2,4,6,7]=>[2,4,3,5,1,6,7]=>[[.,[[.,.],[.,.]]],[.,[.,.]]] [1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,5,1,2,4,7,6]=>[2,4,3,5,1,7,6]=>[[.,[[.,.],[.,.]]],[[.,.],.]] [1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,5,1,2,6,4,7]=>[2,5,3,6,1,4,7]=>[[.,[[.,.],[.,.]]],[.,[.,.]]] [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,5,1,2,6,7,4]=>[2,5,3,7,1,6,4]=>[[.,[[.,.],[.,.]]],[[.,.],.]] [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,5,1,2,7,4,6]=>[2,5,3,6,1,7,4]=>[[.,[[.,.],[.,.]]],[[.,.],.]] [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,5,1,6,2,4,7]=>[5,4,3,6,1,2,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,5,1,6,2,7,4]=>[5,6,3,7,1,2,4]=>[[[.,[.,.]],[.,.]],[.,[.,.]]] [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,5,1,6,7,2,4]=>[5,4,3,7,1,6,2]=>[[[[.,.],.],[.,.]],[[.,.],.]] [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,5,1,7,2,4,6]=>[5,4,3,6,1,7,2]=>[[[[.,.],.],[.,.]],[[.,.],.]] [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,5,6,1,2,4,7]=>[2,4,3,6,5,1,7]=>[[.,[[.,.],[[.,.],.]]],[.,.]] [1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,5,6,1,2,7,4]=>[2,6,3,7,5,1,4]=>[[.,[[.,.],[[.,.],.]]],[.,.]] [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,5,6,1,7,2,4]=>[6,4,3,7,5,1,2]=>[[[[.,.],.],[[.,.],.]],[.,.]] [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,1,2,4]=>[2,4,3,7,5,6,1]=>[[.,[[.,.],[[.,.],[.,.]]]],.] [1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,5,7,1,2,4,6]=>[2,4,3,6,5,7,1]=>[[.,[[.,.],[[.,.],[.,.]]]],.] [1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,6,1,2,4,5,7]=>[2,4,3,5,6,1,7]=>[[.,[[.,.],[.,[.,.]]]],[.,.]] [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,6,1,2,4,7,5]=>[2,4,3,6,7,1,5]=>[[.,[[.,.],[.,[.,.]]]],[.,.]] [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,6,1,2,7,4,5]=>[2,6,3,5,7,1,4]=>[[.,[[.,.],[.,[.,.]]]],[.,.]] [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,6,1,7,2,4,5]=>[6,4,3,5,7,1,2]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,6,7,1,2,4,5]=>[2,4,3,5,7,6,1]=>[[.,[[.,.],[.,[[.,.],.]]]],.] [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,7,1,2,4,5,6]=>[2,4,3,5,6,7,1]=>[[.,[[.,.],[.,[.,[.,.]]]]],.] [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,1,2,3,5,6,7]=>[2,3,4,1,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,1,2,3,5,7,6]=>[2,3,4,1,5,7,6]=>[[.,[.,[.,.]]],[.,[[.,.],.]]] [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,1,2,3,6,5,7]=>[2,3,4,1,6,5,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]] [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,1,2,3,6,7,5]=>[2,3,4,1,7,6,5]=>[[.,[.,[.,.]]],[[[.,.],.],.]] [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,1,2,3,7,5,6]=>[2,3,4,1,6,7,5]=>[[.,[.,[.,.]]],[[.,[.,.]],.]] [1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,1,2,5,3,6,7]=>[2,4,5,1,3,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,1,2,5,3,7,6]=>[2,4,5,1,3,7,6]=>[[.,[.,[.,.]]],[.,[[.,.],.]]] [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,1,2,5,6,3,7]=>[2,4,6,1,5,3,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]] [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,1,2,5,6,7,3]=>[2,4,7,1,5,6,3]=>[[.,[.,[.,.]]],[[.,[.,.]],.]] [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,1,2,5,7,3,6]=>[2,4,6,1,5,7,3]=>[[.,[.,[.,.]]],[[.,[.,.]],.]] [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,1,2,6,3,5,7]=>[2,4,5,1,6,3,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]] [1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,1,2,6,3,7,5]=>[2,4,6,1,7,3,5]=>[[.,[.,[.,.]]],[[.,.],[.,.]]] [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,1,2,6,7,3,5]=>[2,4,5,1,7,6,3]=>[[.,[.,[.,.]]],[[[.,.],.],.]] [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,1,2,7,3,5,6]=>[2,4,5,1,6,7,3]=>[[.,[.,[.,.]]],[[.,[.,.]],.]] [1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,1,5,2,3,6,7]=>[4,3,5,1,2,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,1,5,2,3,7,6]=>[4,3,5,1,2,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]] [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,1,5,2,6,3,7]=>[4,5,6,1,2,3,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[4,1,5,2,6,7,3]=>[4,5,7,1,2,6,3]=>[[.,[.,[.,.]]],[.,[[.,.],.]]] [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,1,5,2,7,3,6]=>[4,5,6,1,2,7,3]=>[[.,[.,[.,.]]],[.,[[.,.],.]]] [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,1,5,6,2,3,7]=>[4,3,6,1,5,2,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]] [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[4,1,5,6,2,7,3]=>[4,6,7,1,5,2,3]=>[[.,[.,[.,.]]],[[.,.],[.,.]]] [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,1,5,6,7,2,3]=>[4,3,7,1,5,6,2]=>[[[.,.],[.,.]],[[.,[.,.]],.]] [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,1,5,7,2,3,6]=>[4,3,6,1,5,7,2]=>[[[.,.],[.,.]],[[.,[.,.]],.]] [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,1,6,2,3,5,7]=>[4,3,5,1,6,2,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]] [1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,1,6,2,3,7,5]=>[4,3,6,1,7,2,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]] [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,1,6,2,7,3,5]=>[4,6,5,1,7,2,3]=>[[.,[[.,.],.]],[[.,.],[.,.]]] [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,1,6,7,2,3,5]=>[4,3,5,1,7,6,2]=>[[[.,.],[.,.]],[[[.,.],.],.]] [1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,1,7,2,3,5,6]=>[4,3,5,1,6,7,2]=>[[[.,.],[.,.]],[[.,[.,.]],.]] [1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[4,5,1,2,3,6,7]=>[2,3,5,4,1,6,7]=>[[.,[.,[[.,.],.]]],[.,[.,.]]] [1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,5,1,2,3,7,6]=>[2,3,5,4,1,7,6]=>[[.,[.,[[.,.],.]]],[[.,.],.]] [1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[4,5,1,2,6,3,7]=>[2,5,6,4,1,3,7]=>[[.,[[.,[.,.]],.]],[.,[.,.]]] [1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[4,5,1,2,6,7,3]=>[2,5,7,4,1,6,3]=>[[.,[[.,[.,.]],.]],[[.,.],.]] [1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,5,1,2,7,3,6]=>[2,5,6,4,1,7,3]=>[[.,[[.,[.,.]],.]],[[.,.],.]] [1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,5,1,6,2,3,7]=>[5,3,6,4,1,2,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]] [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,5,1,6,2,7,3]=>[5,6,7,4,1,2,3]=>[[[.,[.,[.,.]]],.],[.,[.,.]]] [1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,5,1,6,7,2,3]=>[5,3,7,4,1,6,2]=>[[[.,.],[[.,.],.]],[[.,.],.]] [1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,1,7,2,3,6]=>[5,3,6,4,1,7,2]=>[[[.,.],[[.,.],.]],[[.,.],.]] [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,5,6,1,2,3,7]=>[2,3,6,4,5,1,7]=>[[.,[.,[[.,.],[.,.]]]],[.,.]] [1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,1,2,7,3]=>[2,6,7,4,5,1,3]=>[[.,[[.,[.,.]],[.,.]]],[.,.]] [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,1,7,2,3]=>[6,3,7,4,5,1,2]=>[[[.,.],[[.,.],[.,.]]],[.,.]] [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,1,2,3]=>[2,3,7,4,5,6,1]=>[[.,[.,[[.,.],[.,[.,.]]]]],.] [1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,7,1,2,3,6]=>[2,3,6,4,5,7,1]=>[[.,[.,[[.,.],[.,[.,.]]]]],.] [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,6,1,2,3,5,7]=>[2,3,5,4,6,1,7]=>[[.,[.,[[.,.],[.,.]]]],[.,.]] [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,6,1,2,3,7,5]=>[2,3,6,4,7,1,5]=>[[.,[.,[[.,.],[.,.]]]],[.,.]] [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,6,1,2,7,3,5]=>[2,6,5,4,7,1,3]=>[[.,[[[.,.],.],[.,.]]],[.,.]] [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,6,1,7,2,3,5]=>[6,3,5,4,7,1,2]=>[[[.,.],[[.,.],[.,.]]],[.,.]] [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,6,7,1,2,3,5]=>[2,3,5,4,7,6,1]=>[[.,[.,[[.,.],[[.,.],.]]]],.] [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,7,1,2,3,5,6]=>[2,3,5,4,6,7,1]=>[[.,[.,[[.,.],[.,[.,.]]]]],.] [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,1,2,3,4,6,7]=>[2,3,4,5,1,6,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]] [1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,1,2,3,4,7,6]=>[2,3,4,5,1,7,6]=>[[.,[.,[.,[.,.]]]],[[.,.],.]] [1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,1,2,3,6,4,7]=>[2,3,5,6,1,4,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]] [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,1,2,3,6,7,4]=>[2,3,5,7,1,6,4]=>[[.,[.,[.,[.,.]]]],[[.,.],.]] [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,1,2,3,7,4,6]=>[2,3,5,6,1,7,4]=>[[.,[.,[.,[.,.]]]],[[.,.],.]] [1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[5,1,2,6,3,4,7]=>[2,5,4,6,1,3,7]=>[[.,[[.,.],[.,.]]],[.,[.,.]]] [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,1,2,6,3,7,4]=>[2,5,6,7,1,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]] [1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,1,2,6,7,3,4]=>[2,5,4,7,1,6,3]=>[[.,[[.,.],[.,.]]],[[.,.],.]] [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,1,2,7,3,4,6]=>[2,5,4,6,1,7,3]=>[[.,[[.,.],[.,.]]],[[.,.],.]] [1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[5,1,6,2,3,4,7]=>[5,3,4,6,1,2,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,1,6,2,3,7,4]=>[5,3,6,7,1,2,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,1,6,2,7,3,4]=>[5,6,4,7,1,2,3]=>[[[.,[.,.]],[.,.]],[.,[.,.]]] [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,1,6,7,2,3,4]=>[5,3,4,7,1,6,2]=>[[[.,.],[.,[.,.]]],[[.,.],.]] [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[5,1,7,2,3,4,6]=>[5,3,4,6,1,7,2]=>[[[.,.],[.,[.,.]]],[[.,.],.]] [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[5,6,1,2,3,4,7]=>[2,3,4,6,5,1,7]=>[[.,[.,[.,[[.,.],.]]]],[.,.]] [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,6,1,2,3,7,4]=>[2,3,6,7,5,1,4]=>[[.,[.,[[.,[.,.]],.]]],[.,.]] [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,6,1,2,7,3,4]=>[2,6,4,7,5,1,3]=>[[.,[[.,.],[[.,.],.]]],[.,.]] [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,6,1,7,2,3,4]=>[6,3,4,7,5,1,2]=>[[[.,.],[.,[[.,.],.]]],[.,.]] [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,1,2,3,4]=>[2,3,4,7,5,6,1]=>[[.,[.,[.,[[.,.],[.,.]]]]],.] [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[5,7,1,2,3,4,6]=>[2,3,4,6,5,7,1]=>[[.,[.,[.,[[.,.],[.,.]]]]],.] [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,7]=>[2,3,4,5,6,1,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]] [1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,2,3,4,7,5]=>[2,3,4,6,7,1,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]] [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1,2,3,7,4,5]=>[2,3,6,5,7,1,4]=>[[.,[.,[[.,.],[.,.]]]],[.,.]] [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1,2,7,3,4,5]=>[2,6,4,5,7,1,3]=>[[.,[[.,.],[.,[.,.]]]],[.,.]] [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1,7,2,3,4,5]=>[6,3,4,5,7,1,2]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,7,1,2,3,4,5]=>[2,3,4,5,7,6,1]=>[[.,[.,[.,[.,[[.,.],.]]]]],.] [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7,1,2,3,4,5,6]=>[2,3,4,5,6,7,1]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.] [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,6,7,5,8]=>[1,4,3,2,7,6,5,8]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]] [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,4,2,3,7,5,6,8]=>[1,3,4,2,6,7,5,8]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]] [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,5,3,6,4,8,7]=>[2,1,5,6,3,4,8,7]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]] [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,5,3,7,4,8,6]=>[2,1,5,7,3,8,4,6]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]] [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,6,3,7,4,8,5]=>[2,1,6,7,8,3,4,5]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,5,7,8,6]=>[3,2,1,4,5,8,7,6]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]] [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,4,1,6,7,8,5]=>[4,2,3,1,8,6,7,5]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]] [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,5,1,6,7,8,4]=>[5,2,3,8,1,6,7,4]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]] [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,1,2,4,5,8,6,7]=>[2,3,1,4,5,7,8,6]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,4,2,6,5,8,7]=>[3,4,1,2,6,5,8,7]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]] [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,1,4,2,7,5,8,6]=>[3,4,1,2,7,8,5,6]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] [1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,1,5,2,6,4,8,7]=>[3,5,1,6,2,4,8,7]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]] [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,1,5,2,7,4,8,6]=>[3,5,1,7,2,8,4,6]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]] [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,7,1,8,2]=>[7,8,3,4,5,6,1,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,1,2,3,8,5,6,7]=>[2,3,4,1,6,7,8,5]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,1,2,3,8,4,6,7]=>[2,3,5,6,1,7,8,4]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,1,6,2,7,3,8,4]=>[5,6,7,8,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
Map
to 321-avoiding permutation (Krattenthaler)
Description
Krattenthaler's bijection to 321-avoiding permutations.
Map
first fundamental transformation
Description
Return the permutation whose cycles are the subsequences between successive left to right maxima.
Map
to increasing tree
Description
Sends a permutation to its associated increasing tree.
This tree is recursively obtained by sending the unique permutation of length $0$ to the empty tree, and sending a permutation $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.